H∞-FIR filtering of disturbed systems using LMI under measurement and initial errors

Finite impulse response (FIR) filtering is known to be more robust than Kalman filtering. In this article, we derive a discrete convolution-based H infinity$$ {H}_{\infty } $$-FIR observer for disturbed systems under measurement and initial errors. The gain for the H infinity$$ {H}_{\infty } $$-FIR observer is obtained numerically by solving a linear matrix inequality (LMI). Since the LMI has a term that is quadratic with respect to the filter gain, we modify and constrain LMI by introducing an additional variable and proving a theorem. It is shown numerically and experimentally that for disturbed systems operating under measurement and initial errors, the developed H infinity$$ {H}_{\infty } $$-FIR observer surpasses the optimal FIR and Kalman filters in accuracy and has almost the same robustness as a robust unbiased FIR filter.

Automated summary

This article presents a discrete convolution-based H infinity (H∞)-FIR observer for disturbed systems under measurement and initial errors. The gain for the H∞-FIR observer is obtained by solving a linear matrix inequality (LMI) numerically. By introducing an additional variable and proving a theorem, the LMI is modified and constrained to include a quadratic term with respect to the filter gain. Numerical and experimental results demonstrate that the developed H∞-FIR observer outperforms optimal FIR and Kalman filters in accuracy for disturbed systems operating under measurement and initial errors, while maintaining similar robustness to a robust unbiased FIR filter.